Brownian Noise Reduction: Maximizing Privacy Subject to Accuracy Constraints
This work addresses the problem of balancing privacy and accuracy for practitioners in machine learning and data analysis, offering a more flexible and effective approach, though it is incremental as it builds on prior noise reduction methods.
The authors tackled the disconnect between privacy-first and accuracy-first perspectives in privacy-utility tradeoffs by generalizing noise reduction to Gaussian noise, introducing the Brownian mechanism. They showed that this mechanism outperforms existing work on common statistical tasks and provides customizable privacy loss control, meeting utility constraints while maintaining strong privacy levels.
There is a disconnect between how researchers and practitioners handle privacy-utility tradeoffs. Researchers primarily operate from a privacy first perspective, setting strict privacy requirements and minimizing risk subject to these constraints. Practitioners often desire an accuracy first perspective, possibly satisfied with the greatest privacy they can get subject to obtaining sufficiently small error. Ligett et al. have introduced a "noise reduction" algorithm to address the latter perspective. The authors show that by adding correlated Laplace noise and progressively reducing it on demand, it is possible to produce a sequence of increasingly accurate estimates of a private parameter while only paying a privacy cost for the least noisy iterate released. In this work, we generalize noise reduction to the setting of Gaussian noise, introducing the Brownian mechanism. The Brownian mechanism works by first adding Gaussian noise of high variance corresponding to the final point of a simulated Brownian motion. Then, at the practitioner's discretion, noise is gradually decreased by tracing back along the Brownian path to an earlier time. Our mechanism is more naturally applicable to the common setting of bounded $\ell_2$-sensitivity, empirically outperforms existing work on common statistical tasks, and provides customizable control of privacy loss over the entire interaction with the practitioner. We complement our Brownian mechanism with ReducedAboveThreshold, a generalization of the classical AboveThreshold algorithm that provides adaptive privacy guarantees. Overall, our results demonstrate that one can meet utility constraints while still maintaining strong levels of privacy.